Neutrino mass limits and decaying dark matter: background evolution versus perturbations

While decaying dark matter can mimic the background effects of massive neutrinos and allow for eV-scale masses when only distance-based data are used, the inclusion of CMB perturbation observables, particularly lensing, decisively breaks this degeneracy and restores tight neutrino mass constraints.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Mystery: How Heavy are Ghosts?

Imagine the universe is a giant, expanding balloon. Inside this balloon, there are three main ingredients:

1. Normal stuff (stars, planets, us).
2. Dark Matter (invisible "glue" holding galaxies together).
3. Dark Energy (a mysterious force pushing the balloon to expand faster).

For a long time, scientists have been trying to weigh the neutrinos. Neutrinos are like tiny, ghostly particles that zip through everything. We know they have mass, but we don't know exactly how heavy they are.

Recently, scientists looked at the "cosmic map" (data from the Big Bang and galaxy surveys) and found a problem. The map suggests neutrinos are very light (almost weightless). But experiments on Earth suggest they must be heavier than that. It's like a scale saying a feather weighs 10 pounds, while a ruler says it weighs 1 gram. Something is wrong with the scale, or the ruler, or the rules we are using.

The Suspects: Two New Tricks

The authors of this paper asked: "What if our 'cosmic scale' is broken because we are missing a trick in the recipe of the universe?" They tested two new ideas to see if they could fix the weight problem.

Trick 1: The Phantom Energy (Dynamical Dark Energy)

Imagine Dark Energy is a car engine. In the standard model, the engine runs at a constant speed. But what if the engine is actually a variable-speed motor that changes its RPMs over time?

• The Analogy: If the engine speeds up and slows down in a specific way, it can make the universe look like the neutrinos are heavier or lighter than they actually are.
• The Result: This trick helps a little bit. It loosens the rules, allowing neutrinos to be a bit heavier, but it doesn't solve the whole puzzle.

Trick 2: The Leaky Bucket (Decaying Dark Matter)

This is the star of the show. Imagine Dark Matter is a bucket of water. In the standard model, the bucket is solid and never leaks.

• The Analogy: In this new idea, the bucket has a tiny hole. Over billions of years, the water (Dark Matter) slowly leaks out and turns into "dark radiation" (invisible gas).
• Why it matters: When neutrinos get heavy (by slowing down), they make the universe's expansion speed up slightly. But if your Dark Matter bucket is leaking, it slows the expansion down.
• The Magic: The authors found that if you adjust the size of the hole in the bucket just right, the "leak" perfectly cancels out the "weight" of the neutrinos.
• The Result: With this trick, the cosmic data becomes completely blind to the weight of the neutrinos. You could have neutrinos as heavy as a brick (1 eV), and the universe would look exactly the same as if they were weightless. It's like a magician making a heavy elephant disappear by hiding it behind a curtain that moves at the exact same speed as the elephant.

The Plot Twist: The Camera Catches the Lie

So, if the "Leaky Bucket" trick makes the universe look perfect regardless of the neutrino weight, why don't we just accept it? Why do we still have strict limits?

Because the universe has a security camera.

The "background" data (like the size of the balloon) can be fooled by the Leaky Bucket. But there is another type of data: Structure Growth. This is like looking at how the galaxies clump together to form a web.

• The Analogy: Imagine you are trying to hide a heavy rock in a pile of sand.
  • Background View: If you just look at the shape of the pile from far away, the Leaky Bucket trick makes the pile look normal.
  • Structure View: But if you look closely at the sand grains (the galaxies), you see a problem.
    • Heavy neutrinos act like a "brake" on the sand grains, stopping them from clumping together easily.
    • The Leaky Bucket (decaying matter) also acts like a brake, stopping the sand grains from clumping.
  • The Problem: When you combine them, you get double braking. The sand grains stop clumping too much. The "security camera" (CMB lensing data) sees that the galaxy web is too weak and says, "Hey, this doesn't look right!"

The Verdict

The paper concludes with a clear message:

1. If we only look at the "shape" of the universe (Background): The Leaky Bucket trick is amazing. It can hide almost any weight of neutrinos. It even explains some weird tensions in the data better than the Phantom Energy trick.
2. If we look at the "clumping" of the universe (Perturbations): The trick fails. The security camera sees that the galaxy web is too weak.
3. The Final Limit: Once we include the "clumping" data (specifically from the Planck satellite's lensing data), the Leaky Bucket trick is busted. We are forced back to the conclusion that neutrinos must be very light.
   • The Limit: Neutrinos must weigh less than 0.079 eV.

The Takeaway

This paper teaches us a vital lesson about doing science: Don't just look at the big picture; look at the details.

You can build a model that looks perfect from a distance (like a fake painting), but if you zoom in and look at the brushstrokes (the growth of structures), the forgery is revealed. To truly understand the weight of the universe's ghosts, we need to measure not just how the universe expands, but how it builds its structures.

In short: The "Leaky Bucket" is a clever disguise that works on the surface, but the universe's internal structure exposes it, keeping our limits on neutrino mass tight and secure.

Technical Summary

Here is a detailed technical summary of the paper "Neutrino mass limits and decaying dark matter: background evolution versus perturbations" by Montandon et al.

1. Problem Statement

Cosmological observations currently place stringent upper bounds on the sum of neutrino masses ($\sum m_\nu$), typically in the sub-0.1 eV regime (e.g., $\sum m_\nu < 0.048$ eV from DESI BAO + Planck). These bounds are in mild tension with terrestrial lower limits for the "normal ordering" scenario ($\sum m_\nu \gtrsim 0.06$ eV).

Recent analyses combining CMB, DESI BAO, and Type Ia supernovae (SN1a) data have revealed a preference for dynamical dark energy (DDE) with a phantom crossing ($w < -1$ at early times, $w > -1$ at late times) to resolve tensions in the matter density parameter ($\Omega_m$). However, this "mirage dark energy" scenario is considered exotic.

The authors investigate whether alternative extensions to the standard $\Lambda$CDM model, specifically Decaying Dark Matter (DDM), can relax neutrino mass constraints. The core hypothesis is that DDM, which converts matter into dark radiation, might counteract the late-time increase in matter density caused by neutrinos becoming non-relativistic, thereby creating a degeneracy that allows for much larger neutrino masses without degrading the fit to background data.

2. Methodology

The authors perform a comprehensive cosmological parameter estimation using two distinct analytical approaches:

• Models:
  • $\Lambda$CDM: Standard model with stable CDM and massive neutrinos.
  • $\Lambda$DDM: A fraction of CDM decays into massless dark radiation with a constant decay rate $\Gamma$.
  • $w_0 w_a$CDM: Dark energy described by the Chevallier-Polarski-Linder (CPL) parametrization $w(a) = w_0 + w_a(1-a)$.
  • Combined Models: Combinations of DDM and DDE ($w_0$DDM, $w_0 w_a$DDM).
• Datasets:
  • Background-only: Combinations of BAO (DESI DR2), SN1a (Pantheon+), and CMB distance priors (acoustic scale $\theta_*$, $\omega_b$, $\omega_{bc}$).
  • Full CMB: Includes full Planck 2018 (PR3) and NPIPE (PR4) likelihoods (TT, TE, EE spectra) and CMB lensing ($C^{\phi\phi}_\ell$).
• Statistical Framework:
  • Bayesian: MCMC sampling using Cobaya and MontePython.
  • Frequentist: Profile likelihood analysis using bobyqa, PROSPECT, and Procoli to maximize likelihoods over nuisance parameters.
• Tools: Boltzmann solver CLASS for theoretical predictions; analysis performed in Python (Cobaya, MontePython, GetDist).

3. Key Contributions

1. Identification of a Background Degeneracy: The paper demonstrates that for datasets relying solely on background expansion history (geometric probes), there is a nearly exact degeneracy between the sum of neutrino masses and the DDM fraction.
2. Superiority of DDM over DDE in Relaxing Bounds: The authors show that DDM is significantly more effective than DDE (CPL) at relaxing neutrino mass constraints when perturbations are ignored. While DDE allows $\sum m_\nu \sim 0.15-0.20$ eV, DDM allows values up to $\mathcal{O}(1)$ eV without degrading the fit.
3. Breaking the Degeneracy with Perturbations: The study highlights that while DDM and massive neutrinos have opposite effects on the background expansion (DDM reduces effective matter density; neutrinos increase it), their effects on structure growth are cumulative. Both suppress power on small scales.
4. Resolution of the Phantom Crossing: The authors show that including DDM in models with DDE can mimic the phantom behavior ($w < -1$) usually inferred from data, thereby alleviating the need for a phantom crossing while maintaining compatibility with SN1a data.

4. Key Results

A. Background-Only Analysis (BAO + SN1a + CMB Prior)

• Neutrino Mass Constraints:
  • $\Lambda$CDM: $\sum m_\nu < 0.109$ eV.
  • $w_0 w_a$CDM: $\sum m_\nu < 0.158$ eV.
  • $\Lambda$DDM: No meaningful constraint. The posterior is flat up to the prior limit ($\sim 0.9$ eV), and the profile likelihood is flat. The data cannot distinguish between massive neutrinos and DDM at the background level.
• Preference for New Physics:
  • The combination of BAO + CMB prior shows a preference for a non-zero DDM fraction ($f_{\text{DDM}} > 0.013$) with $\Delta \chi^2 \approx -3.6$ relative to $\Lambda$CDM.
  • This preference is slightly reduced ($\Delta \chi^2 \approx -3.0$) when SN1a data is added, but a non-zero DDM fraction remains favored.
  • In combined models ($w_0 w_a$DDM), the DDM component mimics the phantom crossing, allowing $w_0 > -1$ (quintessence-like) to fit the data, removing the need for the "exotic" phantom crossing required in pure DDE models.

B. Full Dataset Analysis (Including CMB Lensing)

• Breaking the Degeneracy:
  • Once CMB lensing and full power spectra are included, the degeneracy is decisively broken.
  • $\Lambda$DDM: The upper bound tightens significantly to $\sum m_\nu < 0.079$ eV (with lensing). This is only $\sim 10\%$ weaker than the standard $\Lambda$CDM bound.
  • $w_0 w_a$CDM: Constraints remain weak ($\sum m_\nu < 0.125$ eV), as smooth dark energy does not significantly alter structure growth.
• Mechanism: Massive neutrinos suppress structure growth via free-streaming. DDM suppresses structure growth because the decay of matter into radiation reduces the gravitational potential wells available for structure formation. Since both effects suppress the matter power spectrum ($P_k$) and CMB lensing potential ($C^{\phi\phi}_\ell$) in the same direction, they cannot compensate for each other; instead, they compound, leading to a strong exclusion of large neutrino masses in the DDM scenario.
• Parameter Constraints:
  • The preference for a non-zero DDM fraction disappears in the full analysis ($f_{\text{DDM}} \lesssim 0.019$).
  • The degeneracy between DDM and phantom dark energy is fully lifted.

5. Significance and Conclusions

• Role of Structure Growth: The paper underscores that structure-growth measurements (specifically CMB lensing) are essential for obtaining robust neutrino mass bounds. Background-only analyses (geometric probes) are insufficient to constrain neutrino masses in the presence of DDM.
• Model Viability: While DDM offers a compelling alternative to DDE for explaining background expansion tensions (like the DESI-Planck tension) without exotic phantom fields, it fails to relax neutrino mass bounds when perturbations are considered.
• Future Directions: The authors suggest that viable extensions to $\Lambda$CDM capable of relaxing neutrino mass bounds must reproduce the background signatures favored by current data (e.g., lower $\Omega_m$) without suppressing the growth of structure. Models that couple dark matter and dark energy non-minimally might possess these specific features, offering a promising avenue for future research.

In summary, the study concludes that while decaying dark matter can effectively hide the background effects of massive neutrinos, the cumulative suppression of structure growth by both mechanisms ensures that current cosmological data still tightly constrains the sum of neutrino masses to $\sum m_\nu \lesssim 0.08$ eV, even in the presence of decaying dark matter.